From the Preface
This Source Book contains selections from mathematical writings of authors in the Latin
world, authors who lived in the period between the thirteenth and the end of the eighteenth
century. By Latin world I mean that there are no selections taken from Arabic or other
Oriental authors, unless, as in the case of Al-Khwarizmi, a much-used Latin translation
was available. The choice was made from books and from shorter writings. Usually only a
significant part of the document has been taken, although occasionally it was possible to include
a complete text. All selections are presented in English translation. Reproductions
of the original text, desirable from a scientific point of view, would have either increased
the size of the book far too much, or made it necessary to select fewer documents in a
field where even so there was an embarras du choix. I have indicated in all cases where the
original text can be consulted, and in most cases this can be done in editions of collected
works available in many university libraries and in some public libraries as well.
It has not often been easy to decide to which selections preference should be given. Some
are fairly obvious; parts of Cardan's ArB magna, Descartes's Geometrie, Euler's MethodUB inveniendi,
and some of the seminal work of Newton and Leibniz. In the selection of other
material the editor's decision whether to take or not to take was partly guided by his personal
understanding or feelings, partly by the advice of his colleagues. It stands to reason
that there will be readers who miss some favorites or who doubt the wisdom of a particular
choice. However, I hope that the final pattern does give a fairly honest picture of the mathematics
typical of that period in which the foundations were laid for the theory of numbers,
analytic geometry, and the calculus.
The selection has been confined to pure mathematics or to those fields of applied mathematics
that had a direct bearing on the development of pure mathematics, such as the
theory of the vibrating string. The works of scholastic authors are omitted, except where,
as in the case of Oresme, they have a direct connection with writings of the period of our
survey. Laplace is represented in the Source Book on nineteenth-century calculus.
Some knowledge of Greek mathematics will be necessary for a better understanding1 of
the selections: Diophantus for Chapters I and II, Euclid for Chapter III, and Archimedes
for Chapter IV. Sufficient reference material for this purpose is found in M. R. Cohen and
I. E. Drabkin, A Bource book in Greek Bcience (Harvard University Press, Cambridge, Massachusetts,
1948). Many of the classical authors are also easily available in English editions,
such as those of Thomas Little Heath.
Author(s): D. J. Struik
Series: Princeton Legacy Library
Publisher: Princeton University Press
Year: 1986
Language: English
Pages: C,XVI,427,B
Tags: History;Mathematics;Science & Math
Abbreviations of Titles
CHAPTER I Arithmetic
Introduction
1. Leonardo of Pisa. The rabbit problem
2. Recorde. Elementary arithmetic
3. Stevin. Decimal fractions
4. Napier. Logarithms
5. Pascal. The Pascal triangle
6. Fermat. Two Fermat theorems and Fermat numbers
7. Fermat. The "Pell" equation
8. Euler. Power residues
9. Euler. Fermat's theorem for n = 3, 4
10. Euler. Quadratic residues and the reciprocity theorem
11. Goldbach. The Goldbach theorem
12. Legendre. The reciprocity theorem
CHAPTER II Algebra
Introduction
1. Al-Khwarizmi. Quadratic equations
2. Chuquet. The triparty
3. Cardan. On cubic equations
4. Ferrari. The biquadratic equation
5. Viète. The new algebra
6. Girard. The fundamental theorem of algebra
7. Descartes. The new method
8. Descartes. Theory of equations
9. Newton. The roots of an equation
10. Euler. The fundamental theorem of algebra
11. Lagrange. On the general theory of equations
12. Lagrange. Continued fractions
13. Gauss. The fundamental theorem of algebra
14. Leibniz. Mathematical logic
CHAPTER III Geometry
Introduction
1. Oresme. The latitude of forms
2. Regiomontanus. Trigonometry
3. Fermat. Coordinate geometry
4. Descartes. The principle of nonhomogeneity
5. Descartes. The equation of a curve
6. Desargues. Involution and perspective triangles
7. Pascal. Theorem on conics
8. Newton. Cubic curves
9. Agnesi. The versiera
10. Cramer and Euler. Cramer's paradox
11. Euler. The Bridges of Königsberg
CHAPTER IV Analysis before Newton and Leinnitz
Introduction
1. Stevin. Centers of gravity
2. Kepler. Integration methods
3. Galilei. On infinites and infinitesimals
4. Galilei. Accelerated motion
5. Cavalieri. Principle of Cavalieri
6. Cavalieri. Integration
7. Fermat. Integration
8. Fermat. Maxima and minima
9. Torricelli. Volume of an infinite solid
10. Roberval. The cycloid
11. Pascal. The integration of sines
12. Pascal. Partial integration
13. Wallis. Computation of p by successive interpolations
14. Barrow. The fundamental theorem of the calculus
15. Huygens. Evolutes and involutes
CHAPTER V Newton, Leibnitz, and Their School
Introduction
1. Leibniz. The first publication of his differential calculus
2. Leibniz. The first publication of his integral calculus
3. Leibniz. The fundamental theorem of the calculus
4. Newton and Gregory. Binomial series
5. Newton. Prime and ultimate ratios
6. Newton. Genita and moments
7. Newton. Quadrature of curves
8. L'Hôpital. The analysis of the infinitesimally small
9. Jakob Bernoulli. Sequences and series
10. Johann Bernoulli. Integration
11. Taylor. The Taylor series
12. Berkeley. The Analyst
13. Maclaurin. On series and extremes
14. D'Alembert. On limits
15. Euler. Trigonometry
16. D'Alembert, Euler, Daniel Bernoulli. The vibrating string and its partial differential equation
17. Lambert. Irrationality of p
18. Fagnano and Euler. Addition theorem of elliptic integrals
19. Euler, Landen, Lagrange. The metaphysics of the calculus
20. Johann and Jakob Bernoulli. The brachystochrone
21. Euler. The calculus of variations
22. Lagrange. The calculus of variations
23. Monge. The two curvatures of a curved surface
Index
